54677 ÷ 5 = 10935 R2
Alright, let's work through the division of 54677 by 5 step by step.

Step 1:
5 goes into 5 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 5 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 5

Step 2:
5 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 4 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 5

Step 3:
5 goes into 46 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 109
Subtract 45 from 46 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 5

Step 4:
5 goes into 17 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 1093
Subtract 15 from 17 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 5

Step 5:
5 goes into 27 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 10935
Subtract 25 from 27 to get 2.

The final result is 10935 with a remainder of 2.